Questions

1. Question 1

   Evaluate each of the following:

   (i)

   $\dfrac{10!}{0!\,8!}$

   (ii)

   $\dfrac{12!}{3!(12-3)!}$

   (iii)

   $\dfrac{1440}{3!\,4!} + \dfrac{2400}{5!\,2!}$

   (iv)

   $\dfrac{(n+2)!}{(n+1)!}$

   SolutionTheory
2. Question 2

   Write each of the following in the factorial form:

   (i)

   $n^3 - n$

   (ii)

   $n(n-1)(n-2)\cdots(n-r+1)$

   SolutionTheory
3. Question 3

   Find $n$, if $(n+4)! = 3024 \cdot n!$.

   SolutionTheory
4. Question 4

   If $\dfrac{1}{7!} + \dfrac{1}{8!} = \dfrac{x}{9!}$, find $x$.

   SolutionTheory
5. Question 5

   Prove that: $\dfrac{(2n+1)!}{n!} = [1\cdot 3\cdot 5\cdots(2n-1)(2n+1)]2^n$.

   SolutionTheory
6. Question 6

   Express as a single fraction: $\dfrac{(n+2)!}{(r+2)!} + \dfrac{(n+1)!}{(r+1)!}$.

   SolutionTheory
7. Question 7

   There are four distinct colored balls and four boxes of same colors as those of the balls. Determine the number of possible ways the balls, one each in a box, can be placed such that a ball does not go to a box of its own colour.

   SolutionTheory